Cooking up pork bones (and fat and other bits) for broth does smell kind of funky, but makes good broth (a lot of ramen is made with pork broth, and may also contain slices of pork). Most split pea soup and clam chowder contain bacon or salt pork. Many soups also feature sausage, for both flavor and texture.
Probably most recipes don't call for the lower-fat cuts of pork though, except to be added at the end because they don't lend much flavor to the broth, and there's a point between just-done and slow-cooked-to-perfection when your meat is just tough-flavorless-protein-that-might-be-pork.

Lots of bean soups are made with ham bones or ham hocks. That's certainly pork. I think there's a (oldd-time) perception that pork was fatty, and so the broth/stock would be too fatty. I've never heard of a consomme or bouillon made with pork, however.

David Chang's Momofuku Ramen Broth made from a pork leg (plus some chicken legs and bacon) is outstanding! Time-consuming but easy to make. We used it to cook up green beans; as a base for noodle soups; to braise some mushrooms; whatever.

Wow, never heard you couldn't! I love Pho and Ramen broths made with pork. And if you're comin' down here to my neck of the woods (Texas), well Greens and Neck Bones with Pot Likker is one of the 8th wonders of the South!